call on the manes

The Oxford English Dictionary nicely captures the rationale for
Victor's use of this Latinism, defining the term in the plural, as

the deified souls of departed ancestors (as beneficent
spirits; opposed to larvŠ and lemures, the malevolent shades of the Lower
World). Also, the spirit, `shade' of a departed person, considered as an
object of homage or reverence, or as demanding to be propitiated by
vengeance.

The manes Victor lists here have in the aggregate constituted the guiding
spirits that throughout this chapter he has invoked as demanding his
intercession to avenge their deaths. Upon his own death he foresees
himself joining their number. If Walton is expected to pick up the family
cause, perhaps in thinking of Victor as "the brother of [his] heart" (Letter 4.5) he has got much more than he
bargained for.